Dynamical entropy of a non-commutative version of the phase doubling

Johan Andries; Mieke De Cock

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 31-40
  • ISSN: 0137-6934

Abstract

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A quantum dynamical system, mimicking the classical phase doubling map z ↦ z 2 on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.

How to cite

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Andries, Johan, and De Cock, Mieke. "Dynamical entropy of a non-commutative version of the phase doubling." Banach Center Publications 43.1 (1998): 31-40. <http://eudml.org/doc/208852>.

@article{Andries1998,
abstract = {A quantum dynamical system, mimicking the classical phase doubling map $z ↦ z^2$ on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.},
author = {Andries, Johan, De Cock, Mieke},
journal = {Banach Center Publications},
keywords = {quantum dynamical entropy; Lyapunov exponent; ergodicity; noncommutative dynamical entropy; partition of unity},
language = {eng},
number = {1},
pages = {31-40},
title = {Dynamical entropy of a non-commutative version of the phase doubling},
url = {http://eudml.org/doc/208852},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Andries, Johan
AU - De Cock, Mieke
TI - Dynamical entropy of a non-commutative version of the phase doubling
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 31
EP - 40
AB - A quantum dynamical system, mimicking the classical phase doubling map $z ↦ z^2$ on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.
LA - eng
KW - quantum dynamical entropy; Lyapunov exponent; ergodicity; noncommutative dynamical entropy; partition of unity
UR - http://eudml.org/doc/208852
ER -

References

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  1. [1] R. Alicki, J. Andries, M. Fannes and P. Tuyls, An algebraic approach to the Kolmogorov-Sinai entropy, Rev. Math. Phys. 8(2) (1996), 167-184. Zbl0884.46039
  2. [2] R. Alicki and M. Fannes, Defining quantum dynamical entropy, Lett. Math. Phys. 32 (1994), 75-82. Zbl0814.46055
  3. [3] J. Andries, M. De Cock and M. Fannes, Preprint K.U. Leuven TF-97/29. 
  4. [4] G.G. Emch, H. Narnhofer, G.L. Sewell and W. Thirring, Anosov actions on noncommutative algebras, J. Math. Phys. 35(11) (1994), 5582-5599. Zbl0817.58028
  5. [5] B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Notes Series 35, Cambridge University Press, Cambridge, 1979. Zbl0423.47001
  6. [6] P. Tuyls, Towards Quantum Kolmogorov-Sinai Entropy, Ph. D. Thesis, K.U. Leuven, 1997. 

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